They constructed the most general coupling of the supersymmetric standard model to supergravity, making the supersymmetry a local symmetry, and employing the super Higgs mechanism and developing the rules of tensor calculus.
[17] In 1992, Chamseddine started to work on a quantum theory of gravity, using the newly developed field of non-commutative geometry, which was founded by Alain Connes, as a suitable possibility.
[18] Together with Jürg Fröhlich and G. Felder, Chamseddine developed the structures needed to define Riemannian noncommutative geometry (metric, connection and curvature) by applying this method to a two-sheeted space.
The fermions come out with the correct representation, and their number is predicted to be 16 per family[21] The advantage of noncommutative geometry is that it provides a new paradigm of geometric space expressed in the language of quantum mechanics where operators replace coordinates.
[24] In recent work, Chamseddine, Alain Connes and Viatcheslav Mukhanov, discovered a generalization of the Heisenberg uncertainty relation for geometry where the Dirac operator takes the role of momenta and the coordinates, tensored with Clifford algebra, serve as maps from the manifold to a sphere with the same dimension.
[25] They have shown that any connected Riemannian Spin 4-manifold with quantized volume appears as an irreducible representation of the two-sided commutation relations in dimensions four[26] with the two kinds of spheres serving as quanta of geometry.